__BANK FINANCIAL MANAGEMENT NUMERICALS : 5__

ABM/BFM NUMERICALS

ABM/BFM NUMERICALS

1. X wants to borrow Rs. 25000 immediately and another Rs. 20000 after a period of 2 years @ 10% roi. He wants to pay it in monthly installments for 5 years. Calculate the amount of monthly payment.

Explanation :

Here, First find PV of 20000 for 2 years @ 10%.

Here, t = 2*12 = 24 months and r = 10% ÷ 12 = 0.00833 PV = P / (1+R)^T So,

PV = 20000 ÷ (1+0.0083)^24

= 16388.07

So, total amount = 25000 + 16388.07 = 41388.07 Now,

P = 41388.07,

R = 10% ÷ 12 = 0.00833,

T = 5 * 12 = 60 months EMI = P * R * [(1+R)^T/(1+R)^T-1)] EMI = (41388.07 * 0.00833) * {(1.0083)^60 ÷ (1.0083)^60 – 1)}

= 879

2. A person wants to receive Rs. 1250 every quarter for 5 years @ 12% roi. How much he should invest now?

Explanation :

Here, P = 1250

R = 12% quarterly = 3% p.a.

T = 5 yrs = 20 quarters PV = P / R * [(1+R)^T - 1]/(1+R)^T So, PV = (1250 ÷ 0.03) * (1.0320 – 1) ÷ 1.0320

= 18597

3. Ranjit borrowed an amount of Rs. 50000 for 8 years @ 18% roi. What shall be monthly payment?

Explanation :

Here, P = 50000

R = 18% = 18 % ÷ 12 = 0.015% monthly

T = 8 yrs = 96 months EMI = P * R * [(1+R)^T/(1+R)^T-1)] EMI = 50000 * 0.015 * 1.01596 ÷ (1.01596 – 1

= 986

4. Ajit wants to receive Rs. 40000 p.a. for 20 years by investing @ 5%. How much he will have to invest now?

Explanation :

Here, P = 40000

R = 5% p.a.

T = 20 yrs PV = P / R * [(1+R)^T - 1]/(1+R)^T PV = (40000 ÷ 0.05) * {(1.0520 – 1) ÷ 1.0520}

= 498489

5. Asha wants to receive a fixed amount for 15 years by investing Rs. 9 lacs @ 9% roi. How much she will receive annually?

Explanation :

Here, P = 9 lac

R = 9% p.a.

T = 15 yrs EMI = P * R * [(1+R)^T/(1+R)^T-1)] EMI = 900000 * 0.09 * 1.0915 ÷ (1.0915 – 1)

= 111653

6. A firm needs Rs. 170000 to replace its machinery at the end of 5 years. At 12% roi, how much it should contribute every month?

Explanation :

Here, FV = 170000

R = 12% p.a. = 0.01% monthly

T = 5 Y = 60 months

(Here, the firm has to contribute monthly, so we have converted rate and time to monthly equivalent values)

FV, if invested at end of each month / year, is: FV = P / R * [(1+R)^T - 1] 170000 = P * (1.0160 -1) ÷ 0.01

170000 = P * 81.66967

P = 170000 / 81.66967

= 2082

7. For carrying out his studies, a student borrows Rs. 3 lac from a bank at concessional rate of 5% p.a. for 4 years of his professional course. What is the total amount payable by him at the end of the 4th year?

Explanation :

Here, P = 3 lac

R = 5% p.a.

T = 4 yrs FV = P / R * [(1+R)^T - 1] FV = 300000*(1.054 – 1) ÷ 0.05

= 1293038

8. X wants to send his daughter to a management school after 5 years and will need onetime payment of charges amounting to Rs. 7 lac. At 12% roi, how much he should invest annually?

Explanation :

Here, FV = 7 lac

R = 12% p.a.

T = 5 yrs FV = P / R * [(1+R)^T - 1] 700000 = P * (1.125 – 1) ÷ 0.12

700000 = P * 6.352847

P = 110187

9. X opened a recurring account with a bank to deposit Rs. 16000 by the end of each year @ 10% roi. How much he would get at the end of 3rd year?

Explanation : Here, P = 16000

R = 10% p.a.

T = 3 yrs FV = P / R * [(1+R)^T - 1] FV = 16000 * (1.13 – 1) ÷ 0.1

= 52960

10. Alka borrowed Rs. 65600 for 2 years at 5% p.a., to be returned in 2 equal installments. What is the amount of installment?

Explanation : Here, P = 65600

R = 5% p.a.

T = 2 yrs EMI = P * R * [(1+R)^T/(1+R)^T-1)] EMI = 65600 × 0.05 × 1.052 ÷ (1.052 – 1)

= 35280

11. Amrita obtained a loan of Rs. 92820 @ 10%, which he has to pay in 4 equal annual installments. Calculate the amount of installment?

Explanation : Here, P = 92820

R = 10% p.a.

T = 4 yrs EMI = P * R * [(1+R)^T/(1+R)^T-1)] EMI = 92820 × 0.1 × 1.14 ÷ (1.14– 1)

= 29282

12. The compound interest on a sum for 2 years is Rs. 153 and simple interest is 225 for 3 years. What are the roi & the principal amount?

Explanation :

Let, principal amount = P,

ROI = R,

simple interest = SI,

compound interest = CI SI for 3 years = 225, so SI for 2 years = 150

CI for 2 years = 153, so difference of Rs. 3 = interest for Rs. 75 (225-150) So, R = 3/75 *100 = 4% P = (SI × 100) ÷ (R×T)

= (225×100) ÷ (4×3)

= 1875

13. X purchased a house and payment terms are - Rs. 10 lac immediately and balance Rs. 7.50 lac after 2 years. The roi is 6% p.a. and to be compounded semi-annually. What is the cash value of the house?

Explanation : Here, PV of Rs. 7.50 lac = 750000 ÷ 1.034 = 666370

So, total cash value = 10 lacs + 666370 = Rs. 16,66,370

14. X had to pay certain amount to z and had 2 options - a) to make payment of lump sum amount of Rs. 120000 immediately or b) to pay Rs. 150000 in 5 years @ 5% p.a. roi (halfyearly compounding). Which option is more beneficial for x?

a. Option a

b. Option b

c. Both are equal

d. None of the above

Ans - b

Explanation : If X goes with option b, PV = 150000 ÷ 1.0255×2 = 117180 which is < 120000. So, option b is more beneficial for X.

15. You will be receiving Rs. 204000 at the end of each year for the next 20 years. If the current discount rate for such a stream of cash is 10%, find the present value of cash flow.

Explanation : Here, Since 204000 is like EMI. So, to find P, we use the formula of EMI EMI = P * R * [(1+R)^T/(1+R)^T-1)] 204000 = P × 0.1 × 1.1^20 ÷ (1.120 – 1)

204000 = P × 0.1174596

P = 1736767

16. You are receiving Rs. 10000 every year for the next 5 years (at the end of the period) and you invest each payment @ 5%. How much you would have at the end of the 5-year period?

Explanation :

Here, P = 10000

R = 5% p.a.

T = 5 yrs If invested at the end, FV = P / R * [(1+R)^T - 1] FV = 10000 × (1.05^5 – 1) ÷ 0.05

= 55256